# QM/MM-embedding for surfaces and solutions

## Development of a QM/MM embedding model for metal oxide surfaces

When studying localized phenomena in solid state it may some times be advantageous to adopt a finite cluster approach rather than the commonly used periodic electronic structure models. However, the construction of the clusters is not straightforward. In particular, designing the so-called embedding, which compensates for the boundary errors in the cluster, requires care and consideration.

We use an embedding scheme which consists of four level, as shown in the picture. Our applications are both MD+QM calculations, and static problems when we need wave function based methods to solve the problem.

In our MD+QM method it is essential that the embedding scheme is both accurate and robust, since we will compare several MD snapshots where the distortions from the ideal geometry may be large, while at the same time the structural changes from one time step to the other may be very modest. We have made efforts to design it in this way.

More details can be found in:

"A combined molecular dynamics + quantum mechanics method for investigation of dynamical effects on local surface structures"

B. Herschend, M. Baudin and K. Hermansson

J. Chem. Phys. 120, 4939-4948 (2004).

## A QM/MM embedding model for ionic solutions

The embedding scheme we have used so far to calculate "in-solution molecular properties" from MD simulation makes use of a two-level model: a supermolecule surrounded by a finite number of point charges. In the example discussed here, it is the uncoupled OH vibrational band for the first-shell water molecules around a cation which is in focus. It is calculated for one OH bond at a time. We find that the long-range interactions die off quite quickly thanks to the disordered structure in the liquid solution; a cut-off radius of less than 15 Å was (usually) found sufficient to converge the O-H frequencies to within 5 wavenumbers. As for the size of the QM cluster, test calculations have shown us that clusters of the form [M(H2O)all first shell(H2O)x]n+, with x = 2 or 3 of the nearest second-shell neighbours, and with x = all of the second hydration-shell waters give essentially the same result. However, when some 4 or 5 of those third-shell neighbours which reside in the vicinity of the vibrating water molecule were incorporated in the QM cluster, the effect was significant (a downshift of several tens of wavenumbers). We conclude that large QM clusters are needed for hydrogen-bonded systems. Moreover, in an MD+QM approach, we have found that the quality of the MD structure, i.e. the force-field, is crucial.

More details are found in:

Pejov et al., J. Phys. Chem. A 109, 5144-5152 (2005) and references therein.